OFFSET
1,3
COMMENTS
The n-odd graph is known to be Hamiltonian for 4 <= n <= 14. Hamiltonian graphs always have a matching with at most one unmatched vertex. - Andrew Howroyd, Mar 23 2018 [Now known for all n >= 4. - Pontus von Brömssen, May 01 2020]
LINKS
T. Mütze, J. Nummenpalo, B. Walczak, Sparse Kneser graphs are Hamiltonian, arXiv:1711.01636, [math.CO], 2017.
Eric Weisstein's World of Mathematics, Independent Edge Set
Eric Weisstein's World of Mathematics, Matching Number
Eric Weisstein's World of Mathematics, Odd Graph
Wikipedia, Odd Graph
FORMULA
a(n) = floor(binomial(2*n - 1, n - 1)/2).
CROSSREFS
KEYWORD
nonn
AUTHOR
Eric W. Weisstein, Mar 23 2018
EXTENSIONS
a(8)-a(14) from Andrew Howroyd, Mar 23 2018
More terms from Pontus von Brömssen, May 01 2020
STATUS
approved